Hand Populous Reincarnated

The Core of the System

Overview
The Populous Reincarnated ranking system was changed early 2010 to a new skill based system instead of the old EA style point-per-win system. The new system is quite a bit more complicated, so this page is to clear up some questions about it. The basis of the ranking system is Trueskill developed by Microsoft Research, and used in the Xbox Live rankings. In turn, that is derived from the Glicko ranking system which is derived from the Elo system. Elo and Glicko are commonly used in Chess and other games to rank players of the matches, however, the system needs to be extended some to account for multiple players on each team as is the case in most Populous games.
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What is μ (mu)?
In Trueskill, players are ranked using Bayesian inference. Now, that sounds pretty complicated, but it can be understood by looking at the part of how it works. In systems like Elo, players are ranked based on one number - their skill level or Elo number. For Trueskill, instead of taking the skill level at face value, it is used as the height of a Gaussian, or Bell curve, with the assumption that the player's skill level is somewhere within that curve. This (mean) average value is known as μ (mu).
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What is σ (sigma)?
But bell curves are not defined by only a mean, they also need a second number to determine the width of the bell curve, so for each player there is a second number to characterize the uncertainty of that skill level called σ (sigma) also known as the standard deviation. As the player plays more games, the uncertainty of their skill will decrease and the bell curve representing their skill will get narrower.
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How are Points Calculated?
Having a bell curve is great to represent the skill of a player. In fact, tests by Microsoft showed that the skill of the player fit into this bell curve 99.99% of the time. However, bell curves aren't very good for easily comparing against each other, so a number is pulled out of this in order to rank players. By subtracting 3*σ from μ, a skill is calculated that is quite a bit lower than the average of the player, but this number is 99.99% sure the player's skill is not any lower than it. To make the numbers easier to read they are multiplied by 10 and so they are all positive (being negative is a bit depressing for bad players), 100 is added. So the final value is:
Points = (μ - 3 * σ) * 10 + 100
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Why not just use the μ (average skill) for the rankings?
For the most part, a ranking that used just the μ value would be the same as subtracting 3 * σ. The only differences appear for new players and cases where one player has played more than another. The σ value will eventually flatten out at around 2 - 3 in this system, so people that play a lot will all be ranked according to their average skill, but when a player is just starting out, their rank will jump up and down a lot until it starts to stabalize on their real skill level. It's better to put an uncertain player at the bottom of their point range, than to put them up higher where more established players will feel their rank is cheapened by being ranked the same. This method also is more heartening for a new player as when playing more games, their rank will keep going up until their rank is more certain, instead of hitting a point and then hopping around a lot.
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Why do players lose points for inactivity?
In order to keep the system accurate, it is assumed that players will become rusty when they don't play. Every day, σ, the uncertainty of a rank,is increased slightly for all players. The increase is small enough that playing a single game will counter it ten-fold, but for players inactiave for long periods of time, it will add up. The mean value is not changed, so playing a few games will bring a previously inactive player back up to the rank they left off with. When a player is inactive for long enough that they reach the starting level of σ (typically about a year), they are no longer shown on the league table. Playing one game will place them back on.
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How long until a player has a rank and is on the league table?
In order to get a rank above wildman and appear on the league table, a player must play a minimum of 10 qualifying games. This number was picked because skill levels start to stablize at around that number of games. That also means that a player of wildman rank is not necessarily worse than a player of brave rank as it was in the old system.
Graph of skill level over time for 100 users:
Rankings over time
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What games do and don't qualify?
Not all games will qualify for the ranking system. Some situations there is no way to compare players in the game so those are not counted. That includes free-for-all games, games where the winners have changed allies (ally-up games), games with no winner due to crashes or network problems, and games with mis-matching winners/losers due to out-of-sync or network problems. Additionally, games with errors in initial reporting by the host will probably not be counted.

Most other games will be counted. If a player quits, crashes, loses internet connection, closes the matchmaker, or changes allies and dies, the game will count as a loss for them as if they died. This is to prevent players from doing any of the above listed in order to prevent the game counting the same as dying.
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How long after a game until the league is updated?
In normal circumstances the league will be updated instantly after all players have finished the game. In cases where one or more players have not reported the game due to network problems or closing the matchmaker, the league will be updated once the missing players report the game, or as soon as any of the players involved in the game completes another game. All non-counted previous games are counted once a game is successfully reported.
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Can points be lost for winning a game?
Generally a player cannot lose points for winning a game, but there are some circumstances that it may happen. If a player has lost a previous game but that game has not yet been counted when the next game ends, both games will be counted at the same time (from oldest to newest) so it may appear that points were lost, even if for that particular game, points were gained. Another common reason for the game results to show points being lost is because of inactiviy being counted as well. Since the comparison is with the previous game played (not the points before the game), there may be an increase in sigma from inactivity counted in the point difference.

There is also a rare situation where there may be a small loss of rank after winning a game if the game is severely imbalanced (such as three shamans allied against a brave).
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How are ranks calculated?
Ranks are based on points. Each rank has a range of 75 points, subdivided into three sections of 25 points. The following graph shows the breakdown of players in each rank:
Ranking distribution
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How many games are needed to get to the next rank?
After 10 games to get past the wildman rank, there isn't a fixed number of games or wins to get to another rank. Depending on the players in games played, new ranks could come in a couple games or not at all. The resulting points as well as μ and σ values can be viewed by typing in some names or numbers in the Skill Calculator.
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Can a player get to the top of the league by beating lots of bad players?
The ranking system scales the amount of points a player will get based on how close the match is. Beating better players gets lots of points, while beating worse players gets little to no points. The graph below shows roughly what the change in points will be for a player based on the difference between the winner and loser points.

Function V

For example, if the winner of the game has 10 points and the loser has only 4, the difference would be 6, so the resulting change in points would be around 0. If the situation is switched around (winner:4, loser:10) then the difference would be -6 and the change in points would be around 7. Note that these numbers are just for example purposes, the input and outputs of the function are slightly more complicated.

A player can only get so far by playing bad players. Eventually they will reach a point where they won't get any higher, and they risk huge losses of points should they ever lose to a low ranked player as shown above.
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How are the best teams calculated?
Best teams are calculated by looking at the game quality for the three possible combinations and selecting the highest one. Game quality is calculated based on both the μ and σ values. Closely matched μ's and low σ's will make the most fair games. Different combinations can be tried out with the Best Team Generator.
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I have an idea to improve the leagues, can I help?
We're always looking for improvements to the system. If you have an idea, feel free to suggest it in the forums or submit a Feature Request. If you want to experiment for yourself, we can provide the game results data in an SQL dump.
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